Abstract #301845

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JSM 2002 Abstract #301845
Activity Number: 409
Type: Contributed
Date/Time: Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing*
Abstract - #301845
Title: An Approximation to the Distribution of the Product of Two Dependent Correlation Coefficients
Author(s): Wei Pan*+ and Kenneth Frank
Affiliation(s): Michigan State University and University of Cincinnati
Address: P.O. Box 210002, Cincinnati, Ohio, 45221, USA
Keywords: approximate distribution ; correlation coefficient ; Pearson distributions
Abstract:

The distribution of correlation coefficients is well studied, but not the distribution of the product of two dependent correlation coefficients. Many methodological studies in the social sciences depend on the product of two dependent correlation coefficients. For example, the impact of a confounding variable in regression analysis (Frank 2000) and indirect effects in path analysis (B. Shipley, personal communication, September 14, 2001). However, the behavior of the distribution of the product of two dependent correlation coefficients is little known. Following Hotelling's (1936, 1940) and Ghosh's (1966) approximations to the moments of the distribution of correlation coefficient, the present study derives an approximation to the distribution of the product of two dependent correlation coefficients with a closed form, resulting in a Pearson Type I (Beta) distribution. A simulation study is also conducted to assess the accuracy of the approximation.

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